Conduits (Pipes) Flow in Closed

7.0 PARAMETERS INVOLVED IN THE STUDY OF FLOW THROUGH
CLOSED CONDUITS

In the previous chapter, the energy level changes along the flow was discussed. The losses due
to wall friction in flows was not discussed. In this chapter the determination of drop in pressure
in pipe flow systems due to friction is attempted.
Fluids are conveyed (transported) through closed conduits in numerous industrial
processes. It is found necessary to design the pipe system to carry a specified quantity of fluid
between specified locations with minimum pressure loss. It is also necessary to consider the
initial cost of the piping system.
The flow may be laminar with fluid flowing in an orderly way, with layers not mixing
macroscopically. The momentum transfer and consequent shear induced is at the molecular
level by pure diffusion. Such flow is encountered with very viscous fluids. Blood flow through
the arteries and veins is generally laminar. Laminar condition prevails upto a certain velocity
in fluids flowing in pipes.
The flow turns turbulent under certain conditions with macroscopic mixing of fluid layers
in the flow. At any location the velocity varies about a mean value. Air flow and water flow in
pipes are generally turbulent.
The flow is controlled by (i) pressure gradient (ii) the pipe diameter or hydraulic
mean diameter (iii) the fluid properties like viscosity and density and (iv) the pipe
roughness. The velocity distribution in the flow and the state of the flow namely laminar or
turbulent also influence the design. Pressure drop for a given flow rate through a duct for a
specified fluid is the main quantity to be calculated. The inverse-namely the quantity flow for
a specified pressure drop is to be also worked out on occasions.
The basic laws involved in the study of incompressible flow are (i) Law of conservation
of mass and (ii) Newton s laws of motion.
Besides these laws, modified Bernoulli equation is applicable in these flows.
7.4 FEATURES OF LAMINAR AND TURBULENT FLOWS

In laminar region the flow is smooth and regular. The fluid layers do not mix macroscopically
(more than a molecule at a time). If a dye is injected into the flow, the dye will travel along a
straight line. Laminar flow will be maintained till the value of Reynolds number is less than of
the critical value (2300 in conduits and 5 × 10 5 in flow over plates). In this region the viscous
forces are able to damp out any disturbance.

The friction factor, f for pipe flow defined as 4?? s/(?u 2/2g o) is obtainable as f = 64/Re
where???? s is the wall shear stress, u is the average velocity and Re is the Reynolds number. In
the case of flow through pipes, the average velocity is used to calculate Reynolds number.

In turbulent flow there is considerable mixing between layers. A dye injected into the
flow will quickly mix with the fluid. Most of the air and water flow in conduits will be turbulent. Turbulence leads to higher frictional losses leading to higher pressure drop. The friction factor is given by the following empirical relation